triangle ABC A is (-3,1) B is (5,-3) C is (1,7)

find the equations of:
the median AM
And
the perpendicular bisector of BC

Middle of BC is

( (1+5)/2 , (-3+7)/2) )
or
(3,2) is point M
so
line through (-3,1) and (3,2)
I bet you can find that line.

Then
line through M perpendicular to BC
slope of BC = 10/-4 = -5/2
so slope we want = 2/5
so line with m = 2/5 that goes through (3,2)
I bet you can do that too.